Interferometers commonly use polarization encoding to distinguish reference beams from measurement beams. In a plane-mirror interferometer 100 illustrated in FIG. 1, for example, an input beam IN contains two linearly polarized components having orthogonal linear polarizations. A polarizing beam splitter 110 in interferometer 100 separates the two components creating a reference beam and a measurement beam.
In FIG. 1, polarizing beam splitter 110 reflects the component corresponding to the reference beam. The reference beam thus travels down a path R1 through a quarter-wave plate 120 to a reference mirror 130. Reference mirror 130 has a fixed mounting relative to polarizing beam splitter 110 and is aligned perpendicular to path R1 so that the reference beam reflects from a reference mirror 130 and travels back through quarter-wave plate 120 along path R1. Passing twice through quarter-wave plate 120 effectively rotates the polarization of the reference beam by 90° so that the reference beam returning on path R1 passes through polarizing beam splitter 110 and enters a cube comer reflector 140 along a path R2.
Cube comer reflector 140 reflects the reference beam onto an offset path R3, and the reference beam traverses polarizing beam splitter 110 directly to a collinear path R4. The reference beam then continues along a path R4 through quarter-wave plate 120 before again reflecting from reference mirror 130 and returning through quarter-wave plate 120 along path R4. The second pair of trips through quarter-wave plate 120 changes the polarization of the reference beam, so that polarizing beam splitter 110 reflects the reference beam from path R4 onto an output path ROUT.
Polarizing beam splitter 110 of FIG. 1 transmits the input polarization component corresponding to the measurement beam so that the measurement beam travels along a path M1 through a quarter-wave plate 150 to a measurement mirror 160. Measurement mirror 160 is on an object such as a translation stage in processing equipment for integrated circuit fabrication. Measurement mirror 160 is ideally perpendicular to path M1, but generally, measurement mirror 160 may have an angular orientation that is subject to variations as the object moves. FIG. 1 shows a configuration where measurement mirror 160 has a non-zero yaw angle relative to path M1. As a result, the measurement beam reflected from measurement mirror 160 returns along a path M1′ that forms a non-zero angle (i.e., twice the yaw angle) with path M1.
The measurement beam, which passed twice through quarter-wave plate 150, had its linear polarization rotated by 90°, so that polarizing beam splitter 110 reflects the measurement beam from path M1′ to a path M2 into cube corner 140. From cube corner 140, the measurement beam travels path M3, reflects in polarizing beam splitter 110 to a path M4 through quarter-wave plate 150 to measurement reflector 160. The measurement beam then returns from measurement reflector along a path M4′ through quarter-wave plate 150. Path M4′ forms an angle with path M4 according to the orientation of measurement mirror 160 and is parallel to path M1. Polarizing beam splitter 110 transmits the measurement beam from path M4′ to an output path MOUT.
Interferometer electronics (not shown) can analyze phase information from a combination of the reference and measurement beams to measure movement of measurement mirror 160. In particular, a combined beam resulting from combining the reference and measurement beams can be made to interfere to produce a measurement signal. Each reflection of the measurement beam from measurement mirror 160 when measurement mirror 160 is moving along the direction of the measurement beam causes a Doppler shift in the frequency of the measurement beam and a corresponding change in the beat frequency of the combined beam. In a DC interferometer where the measurement and reference beams initially have the same frequency, the beat frequency of the combined beam corresponds to the Doppler shift. In an AC interferometer where the measurement and reference beams initially have slightly different frequencies, the change in the beat frequency indicates the Doppler shift.
AC interferometers typically use an input beam having orthogonal, linear polarization components with slightly different frequencies. Imperfect polarization separation of the frequency components of the input beam can cause cyclic errors in the Doppler shift measurement. If the reference beam, for example, contains some light at the frequency intended for the measurement beam, the reference beam by itself gives rise to an error signal having the beat frequency depending on the frequencies of the input components. If the error signal becomes too large when compared to the measurement signal accurate measurements become difficult. Accordingly, maximizing the measurement signal is important for accurate measurements.
Maximizing the measurement signal for AC or DC interferometers requires efficient combination of the measurement and reference beams, and combination of the reference and measurement beams is most efficient when the output paths ROUT and MOUT for the reference and measurement beams are collinear. Achieving collinear output beams from interferometer 100 depends on proper alignment of reference mirror 130 and measurement mirror 160.
In the properly aligned configuration, measurement mirror 160 is perpendicular to path M1, and reflected paths M1′ and M4′ are collinear with incident paths M1 and M4. As a result, measurement paths M2, M3, and MOUT respectively coincide with reference paths R2, R3, and ROUT when measurement mirror 160 is ideally aligned. If measurement mirror 160 is out of alignment, paths M1 and M1′ form an angle that depends on the misalignment of measurement mirror 160, and the reference and measurement paths are skewed relative to each other. The angular misalignment or angular difference between the measurement and reference paths continues until the second reflection from measurement mirror 160 at which point measurement path M4′ and output path MOUT become parallel to the output path ROUT for the reference beam. However, the angular variation of measurement mirror 160 still displaces the measurement beam output path MOUT relative to the reference beam output path ROUT. This phenomenon is commonly referred to as beam walk-off.
When the beam walk-off is negligible compared to the diameters for the reference and measurement beams, the combined beam provides a strong measurement signal. However, a misalignment of measurement mirror 160 by about 0.001 radians or more in concert with a large distance (on the order of 0.5 meters or more) between beam splitter 110 and mirror 160 in some precision interferometers causes a walk-off that is a significant fraction of the beam diameters. (The walk-off in a plane-mirror interferometer is generally about 4 Lα, where L is the distance between the interferometer and measurement mirror 160 and α is the angular misalignment of measurement mirror 160.) The resulting decrease in the overlapped area of the measurement and reference beams causes a significant drop off in the measurement signal, making the cyclic error signal more significant and making accurate measurements difficult.
Another problem arising from beam walk-off is the dynamic range of measurement signal during operation of interferometer 100. In particular, the light intensity in the overlapped beam can vary from a best case having a maximum overlap to a worst-case have a relatively small overlap. The intensity of the measurement signal thus depends on the alignment of measurement mirror 160, and the alignment changes during operation of interferometer 100, particularly when the object being measured moves. The input beam must have sufficient power to provide a measurable signal in the worst-case alignment, which significantly reduces energy efficiency of interferometer 100. Additionally, the optical receiver and measurement electronics must have a dynamic range sufficient to handle both the worst case low measurement signal levels and best case high measurement signal levels.
Yet another drawback of beam walk-off arises from non-uniformity of the wave fronts of the beams. Typically, beam curvature, wedge angles, and aberrations of the beams themselves and optical surfaces traversed by one beam but not by the other can cause wave front phase differences. Measurement beam walk-off can change the overlap and specifically cause the measured phase of the signal to change even if the distance between mirror 160 and beam splitter 110 did not change.
Interferometer 100 employs cube corner reflector 140 to redirect the reference and measurement beams for additional reflections from respective plane-mirror reflectors 130 and 160. As noted above, cube corner reflector 140 and the additional reflections avoid angular separations between output beam paths ROUT and MOUT. The additional reflections also increase (i.e., double) the Doppler shift of the measurement beam and can increase the measurement resolution of the interferometer. A further cube corner reflector might be added to further increase the number of reflections of the measurement beam from measurement reflector 160 (and the number of reflections of the reference beam from the reference reflector 130). A shortcoming of using a cube corner reflector is the resulting increase in the beam walk-off (e.g., doubling beam walk-off when doubling the number of reflections).
A dynamic beam steering system could measure the relative position of the measurement and reference beams during operation of interferometer 100 and then dynamically adjust reference mirror 130 or another optical element in interferometer 100 to minimize the walk-off. Such dynamic steering systems tend to be complex, expensive, and vulnerable to failure. Accordingly, more efficient and less complex systems and methods for reducing or eliminating walk-off are desired.